High performance sensor systems are typically based on closed loop architectures to provide good linearity and large dynamic range. Systems typically use sigma-delta modulated single-bit feedback and let the sensing element act as a loop filter. A voltage driven micro-machined inertial sensor acts as a second order low pass filter where one order comes from the voltage to force (charge) conversion and the other order from force to displacement which is what is detected. FIG. 1 is an illustrative example of a prior art system 10 of a second order accelerometer system. The prior art technology of FIG. 1 limits the noise-shaping order of the system to two. One drawback is that the system 10 requires a large over-sampling ratio to achieve low in-band quantization noise density. A large over-sampling ratio drives up the power consumption mainly due to the charging and discharging of the force capacitors. The high-frequency phase-shift of the sensing element is close to 180 degrees. Therefore, a power-consuming phase compensating lead-lag is required to guarantee stability of the system. In most applications, e.g. battery operated, the power consumption can be equally or even more important than the signal-to-noise ratio.
The required over-sampling ratio can be decreased by adding electrically determined poles to the transfer function of the system which increases the noise shaping order. The systems create a fifth order system by introducing three electrical poles. They still use single-bit feedback to the sensing element and they also make use of a phase compensating filter to ensure stability.
The prior art systems use single-bit feedback. Single-bit noise shapers possess two attractive properties namely simplicity and linearity. It is significantly easier to build a single-bit quantizer than a multi-bit quantizer both in terms of quantization levels and power consumption. A single-bit feedback system is inherently more linear than a multi-bit system since mismatch of the feedback signal is no issue with only two levels. However, single-bit feedback systems are always be a compromise between quantization of the noise performance and the over-sampling ratio, i.e. power consumption. There is a need for a more effective system that operates reliably without suffering from the drawbacks described above.